Elliptic curve isogeny class 1331.1-b over number field \(\Q(\sqrt{3}) \)

• Base field: \(\Q(\sqrt{3}) \)
• Label: 2.2.12.1-1331.1-b
• Conductor: 1331.1
• Rank: \( 0 \)

Base field \(\Q(\sqrt{3}) \)

Generator \(a\), with minimal polynomial \( x^{2} - 3 \); class number \(1\).

Rank

Rank: \( 0 \)

Isogeny matrix

\(\left(\begin{array}{rrrr} 1 & 4 & 2 & 4 \\ 4 & 1 & 2 & 4 \\ 2 & 2 & 1 & 2 \\ 4 & 4 & 2 & 1 \end{array}\right)\)

Isogeny graph

Elliptic curves in class 1331.1-b over \(\Q(\sqrt{3}) \)

Isogeny class 1331.1-b contains 4 curves linked by isogenies of degrees dividing 4.

Curve label	Weierstrass Coefficients
1331.1-b1	\( \bigl[a\) , \( a\) , \( 0\) , \( -18 a - 158\) , \( 2237 a + 4468\bigr] \)
1331.1-b2	\( \bigl[a\) , \( a\) , \( 0\) , \( -13 a - 23\) , \( -18 a - 31\bigr] \)
1331.1-b3	\( \bigl[a\) , \( a\) , \( 0\) , \( -133 a - 238\) , \( 1012 a + 1764\bigr] \)
1331.1-b4	\( \bigl[a\) , \( a\) , \( 0\) , \( -2168 a - 3758\) , \( 70587 a + 122280\bigr] \)